## Problem 2044

Find the equation of a line that passes through (2,14) and is parallel to the graph of y = 3x +4.

Write the equation in slope-intercept form.

**Solution:-**

If the slope and a point on the line are known, we can find the equation of the line in slope-intercept form.

Parallel lines have the same slope. Therefore, the slope of the line that is parallel to the given line, y = 3x +4, is 3.

Find the equation of the line that passes through the point (2,14) with a slope of 3. Substitute 2 for x_{1}, 14 for y_{1}, and 3 for m into point-slope form.

y– y_{1 }= m(x-x_{1})

y – 14 = 3(x – 2)

Solve the equation for y.

y – 14 = 3(x – 2)

y – 14 = 3x – 6

y = 3x + 8

Thus, the equation of the desired line is y = 3x + 8.